“I’m a definite maybe,” said Mr. Chaffetz in a telephone interview with The Washington Times. “I have been thinking about it, and I have increasing clarity about it. I’m definitely leaning toward it.”

Mr. Chaffetz said he doesn’t plan to announce his decision until after Labor Day, adding that, “Elections are long enough already.”

The 44-year-old Mr. Chaffetz may seem like a bit of an upstart - he’s serving only his second House term after working previously as Gov. John Huntsman Jr.’s chief of staff - but he’s already won plaudits from conservatives as part of the young cadre of budget-cutting fiscal hawks.

Even though nothing’s official, Mr. Chaffetz has been all but endorsed by the Club for Growth, which played a crucial role in the defeat of Mr. Bennett in 2010. Club for Growth President Chris Chocola said Wednesday that if Mr. Chaffetz decides to run, he would have “the full support of the Club for Growth PAC and our 55,000 members.”

Last year, the Club for Growth spent nearly $200,000 on an anybody-but-Bennett campaign, more than all but one of Mr. Bennett’s five primary challengers. Mr. Bennett ultimately finished third in the primary balloting at the Republican state convention.

Former Assistant U.S. Attorney Mike Lee won the Senate seat after defeating businessman Tim Bridgewater in a runoff for the nomination.

“Run, Jason, run!” said Club for Growth President Chris Chocola in a statement.“Congressman Chaffetz has been a pro-growth star since entering the House, and hes exactly the type of leader we need in the United States Senate.”

Polls have already shown Mr. Hatch, 76, trailing in hypothetical primary matchups against Mr. Chaffetz and Mr. Huntsman, a former ambassador to China and a potential presidential candidate. Utah state Sen. Dan Liljenquist is reportedly weighing a run for the nomination as well.

Mr. Lee has pointedly declined to endorse Mr. Hatch, saying he wants to see the primary process play out. Mr. Hatch received a rough reception in February at the Conservative Political Action Committee meeting, where the crowd heckled him for his support of the federal TARP bailout.

Still, Mr. Hatch isn’t going down without a fight. Conservatives have griped for years about the senator’s tendency to stray leftward, but Mr. Hatch earned a perfect 100 percent score from the American Conservative Union in 2010, bringing his lifetime rating to 89.7 percent.

Mr. Chaffetz ticked off a list of issues on which he disagrees with Mr. Hatch, including his support for the TARP bailout, the Freddie Mac and Fannie Mae bailout, No Child Left Behind, the individual health-care mandate, and immigration.

“Most of these are causing the problems that we’re facing today,” said Mr. Chaffetz. “If you want a different result, you’re going to have to elect different people.”